A type system for PSPACE derived from light linear logic

We present a polymorphic type system for lambda calculus ensuring that well-typed programs can be executed in polynomial space: dual light affine logic with booleans (DLALB). To build DLALB we start from DLAL (which has a simple type language with a linear and an intuitionistic type arrow, as well as one modality) which characterizes FPTIME functions. In order to extend its expressiveness we add two boolean constants and a conditional constructor in the same way as with the system STAB. We show that the value of a well-typed term can be computed by an alternating machine in polynomial time, thus such a term represents a program of PSPACE (given that PSPACE = APTIME). We also prove that all polynomial space decision functions can be represented in DLALB. Therefore DLALB characterizes PSPACE predicates.Comment: In Proceedings DICE 2011, arXiv:1201.034

The Inflaton Portal to Dark Matter

We consider the possibility that the inflaton is part of the dark sector and interacts with the standard model through a portal interaction with a heavy complex scalar field in equilibrium with the standard model at high energies. The inflaton and dark matter are encapsulated in a single complex field and both scalar sectors are charged under different (approximate) global U(1)'s such that the dark matter, as well as the visible pseudo-scalar are taken to be relatively light, as pseudo Nambu-Goldstone bosons of the theory. The dark matter relic density is populated by Freeze-In productions through the inflaton portal. In particular, after the reheating, production of dark matter by inflaton decay is naturally suppressed thanks to Planck stringent constraints on the dark quartic coupling, therefore preserving the non thermal scenario from any initial condition tuning.Comment: 11 pages, 5 figures, citations added, typos corrected, comments adde

Enumeration of nilpotent loops up to isotopy

We modify tools introduced by Daniel Daly and Petr Vojtechovsky in order to count, for any odd prime q, the number of nilpotent loops of order 2q up to isotopy, instead of isomorphy.Comment: 20 pages; important typos corrected (section 6

About the non-asymptotic behaviour of Bayes estimators

This paper investigates the {\em nonasymptotic} properties of Bayes procedures for estimating an unknown distribution from $n$ i.i.d.\ observations. We assume that the prior is supported by a model (\scr{S},h) (where $h$ denotes the Hellinger distance) with suitable metric properties involving the number of small balls that are needed to cover larger ones. We also require that the prior put enough probability on small balls. We consider two different situations. The simplest case is the one of a parametric model containing the target density for which we show that the posterior concentrates around the true distribution at rate $1/\sqrt{n}$. In the general situation, we relax the parametric assumption and take into account a possible mispecification of the model. Provided that the Kullback-Leibler Information between the true distribution and \scr{S} is finite, we establish risk bounds for the Bayes estimators.Comment: Extended version of a talk given in June 2013 at BNP9 Conference in Amsterdam - 17 page